Question 1

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

Accepted Answer

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Question 2

Mary needs a pension that will pay her $12,000 one year from now and annual payments for 24 more years that are each 5% larger than the previous year. If the funds in her Retirement Fund earn 7.5% compounded annually, how much money must she have there now?

Accepted Answer

The answer of Mary needs a pension that will pay...

Question 3

An 18-year-old college student plans to save a "Buck-A-Day" in a glass jar and after one year, set up a Retirement Savings Plan with $365. One year later he will make his second contribution to the RSP but it will be 10% larger than the first one. He will continue to increase his annual contributions by 10%. He anticipates that his investments can earn an annual return of 12.5% compounded annually. How much money is he expecting to have in the RSP after 40 years?

Accepted Answer

The answer of An 18-year-old college student plans to save...

Question 4

A loan of $126,500,000 is to be repaid by annual payments for 25 years. The payments will form a constant growth annuity with each payment being 20% larger than the previous one. The interest rate charged on the loan is 11% compounded annually. What is the size of the first payment?

Accepted Answer

The first payment is $1,890,589. This is because the present value of the annuity is $126,500,000, and the interest rate is 11%. The first payment is then calculated as follows:PV = PMT * [1 - (1 + r)^-n] / r$126,500,000 = PMT * [1 - (1 + 0.11)^-25] / 0.11PMT = $1,890,589

Question 5

We will make annual RRSP contributions at the end of every year for 35 years and each contribution is going to be 8% larger than the previous one. Our goal is to have $2,000,000 in 35 years. The RRSP will earn 13% compounded annually. How large will the first contribution be?

Accepted Answer

The answer of We will make annual RRSP contributions at...

Question 6

What amount of money invested now will provide monthly payments of $200 for five years, if the ordinary annuity is deferred for 3½ years and the money earns 3.75% compounded monthly?

Accepted Answer

The answer of What amount of money invested now will...

Question 7

Christian plans to initially contribute $3,000 and increase his yearly contributions by 5% each year for 20 years. If the rate of interest is 7% compounded annually, determine the amount of his payment in year 12.

Accepted Answer

The correct answer is A.The amount of his payment in year 12 is $5,387.56.The formula for the future value of an annuity is:FV = P * [(1 + r)^n - 1] / rwhere:* FV is the future value of the annuity* P is the annual payment* r is the annual interest rate* n is the number of yearsIn this case, we have:* P = $3,000* r = 7%* n = 20So, the future value of the annuity is:FV = $3,000 * [(1 + 0.07)^20 - 1] / 0.07 = $86,206.56The amount of his payment in year 12 is:$86,206.56 / (1 + 0.07)^12 = $5,387.56

Question 8

Marion's grandfather will establish a trust that will pay her $1,500 every three months for 11 years. The first payment will be made six years from now, when she turns 19. If money is worth 6.5% compounded quarterly, what is today's economic value of the bequest?

Accepted Answer

The answer of Marion's grandfather will establish a trust that...

Question 9

We are aiming to have $5,000,000 in 45 years and we plan to get there by making monthly investments that are 1% larger than the previous month's investment. Our funds will earn 14.4% compounded monthly. How much should be invested at the end of the first month?

Accepted Answer

The problem can be solved using the future value of a growing annuity formula, which is $FV = P \times \frac{(1 + r)^n - (1 + g)^n}{r - g}$, where $FV$ is the future value, $P$ is the payment at the end of the first period, $r$ is the monthly interest rate, $n$ is the total number of payments, and $g$ is the growth rate of the payment. Given a 14.4% annual interest rate compounded monthly, $r = \frac{14.4\%}{12} = 0.012$, and a growth rate of 1% per month, $g = 0.01$. The total number of payments over 45 years, with 12 payments per year, is $n = 45 \times 12 = 540$. We aim for a future value ($FV$) of $5,000,000. Plugging these values into the formula and solving for $P$ gives us the initial investment amount required to meet the goal.

Question 10

Barklay has $782,490 in his Retirement Saving Plan and he wants to start receiving income at the end of every three months for the next 22 years. The funds earn 7% compounded quarterly and he wants each payment that he receives to be 1.5% larger than the previous one. How much will the first payment be three months from now?

Accepted Answer

The answer of Barklay has $782,490 in his Retirement Saving...

Question 11

Using an inheritance he recently received, Sam wants to purchase a deferred annuity that will pay $5,000 every three months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first payment will be received three months after he reaches 60, and the last payment will be received on his 65^th birthday. If Sam's current age is 50 years and 6 months and the invested funds will earn 4.4% compounded quarterly, what amount must he invest in the deferred annuity?

Accepted Answer

The answer of Using an inheritance he recently received, Sam...

Question 12

An investment of $50 is to be made at the end of this month and that amount is increased by 1% every month for 40 years. The investments are expected to earn 13.2% compounded monthly. What should be the total value of these investments in 40 years?

Accepted Answer

The correct answer is A. The total value of these investments in 40 years is $3,607,093.

Question 13

How much money would accumulate over 35 years if the investor makes an investment of $3,500 at the end of the first year and always increases the size of the annual investment by 5% over the previous year. The investments are expected to earn 11% compounded annually.

Accepted Answer

The future value of a growing annuity formula is used to calculate the accumulated amount. The formula considers the initial investment, growth rate of the investment, interest rate, and the number of periods. Using these values, the correct calculation results in $1,928,432.

Question 14

Edward wishes to have $450,000 in his retirement plans in 25 years. He plans to make annual contributions that will increase by 1% each year. If interest is earned at 5% compounded annually, determine the value of the initial payment in year 1.

Accepted Answer

The answer of Edward wishes to have $450,000 in his...

Question 15

What amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 5.4% compounded monthly.

Accepted Answer

The answer of What amount of money invested now will...

Question 16

Nino plans to initially contribute $10,000 and increase his yearly contributions by 2% each year for 15 years. If the rate of interest is 4% compounded annually, determine how much the investment will be worth in 15 years.

Accepted Answer

The future value of a growing annuity formula is used here. The initial contribution is $10,000, growing at 2% annually, with a 4% interest rate compounded annually over 15 years. Calculating this gives approximately $227,537.58.

Question 17

Baba Lou plans to retire in 20 years. At that point, he plans to collect payments at the end of every six months that are 2% larger than the previous payment, and this is to continue for 30 years. The first payment will be $16,500. His retirement plan is expected to earn 7% compounded semi-annually after he retires and 10% compounded annually before he retires. What single investment should he make now to fund the whole retirement plan?

Accepted Answer

The answer of Baba Lou plans to retire in 20...

Question 18

How much will it cost to purchase a 20-year indexed annuity in which the end of quarter payments start at $6,000 and grow by 0.5% every quarter? Assume that the money used to purchase the annuity earns 8% compounded quarterly.

Accepted Answer

The correct answer is A because the present value of the annuity is $277,727. The present value of an indexed annuity can be calculated using the following formula:PV = PMT * (1 - (1 + g)^-n) / (r - g)where:PMT = the starting paymentg = the growth raten = the number of paymentsr = the discount rateIn this case, the starting payment is $6,000, the growth rate is 0.5%, the number of payments is 80 (20 years * 4 quarters per year), and the discount rate is 8%. Plugging these values into the formula, we get:PV = $6,000 * (1 - (1 + 0.005)^-80) / (0.08 - 0.005)= $277,727

Question 19

Mr. Haddit plans to retire eight years from today. He projects that he will need $30,000 per year in his retirement which he assumes will be for 15 years. The first payment will be nine years from today. To fund his retirement, Mr. Haddit will invest a lump amount today and later use it to sustain the 15 withdrawals. If his investment earns 6% compounded annually, how much must he invest today?

Accepted Answer

The answer of Mr. Haddit plans to retire eight years...

Question 20

Calculate the present value of a 25-year annuity making semi-annual payments that grow at a rate of 4% compounded annually. The first payment is $25,000 and the funds earn 8% compounded semi-annually.

Accepted Answer

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Quiz 12: Annuities: Special Situations